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Abstract: The final solution set given by almost all existing preference-based multi-objective evolutionary algorithms (MOEAs) lies a certain distance away from the decision makers’ preference information region. Therefore, we propose a multi-objective optimization algorithm, referred to as the double-grid interactive preference based MOEA (DIP-MOEA), which explicitly takes the preferences of decision makers (DMs) into account. First, according to the optimization objective of the practical multi-objective optimization problems and the preferences of DMs, the membership functions are mapped to generate a decision preference grid and a preference error grid. Then, we put forward two dominant modes of population, preference degree dominance and preference error dominance, and use this advantageous scheme to update the population in these two grids. Finally, the populations in these two grids are combined with the DMs’ preference interaction information, and the preference multi-objective optimization interaction is performed. To verify the performance of DIP-MOEA, we test it on two kinds of problems, i.e., the basic DTLZ series functions and the multi-objective knapsack problems, and compare it with several different popular preference-based MOEAs. Experimental results show that DIP-MOEA expresses the preference information of DMs well and provides a solution set that meets the preferences of DMs, quickly provides the test results, and has better performance in the distribution of the Pareto front solution set.

DIP-MOEA：一种形式化表达决策者偏好的双重网格交互偏好多目标进化算法

[1]Akram M, Kahraman C, Zahid K, 2021. Group decision-making based on complex spherical fuzzy VIKOR approach. Knowl-Based Syst, 216:106793.

[2]Altuzarra A, Moreno-Jiménez JM, Salvador M, 2007. A Bayesian priorization procedure for AHP-group decision making. Eur J Oper Res, 182(1):367-382.

[3]Bazgan C, Hugot H, Vanderpooten D, 2009. Solving efficiently the 0–1 multi-objective knapsack problem. Comput Oper Res, 36(1):260-279.

[4]Cai XY, Xiao YS, Li MQ, et al., 2021. A grid-based inverted generational distance for multi/many-objective optimization. IEEE Trans Evol Comput, 25(1):21-34.

[5]Champasak P, Panagant N, Pholdee N, et al., 2020. Self-adaptive many-objective meta-heuristic based on decomposition for many-objective conceptual design of a fixed wing unmanned aerial vehicle. Aerosp Sci Technol, 100:105783.

[6]Chen XQ, Lai CS, Ng WWY, et al., 2021. A stochastic sensitivity-based multi-objective optimization method for short-term wind speed interval prediction. Int J Mach Learn Cybern, 12(9):2579-2590.

[7]Cheng R, Jin YC, Olhofer M, et al., 2016. A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput, 20(5):773-791.

[8]Chiu WY, Manoharan SH, Huang TY, 2020. Weight induced norm approach to group decision making for multi-objective optimization problems in systems engineering. IEEE Syst J, 14(2):1580-1591.

[9]Cui ZH, Zhang JJ, Wu D, et al., 2020. Hybrid many-objective particle swarm optimization algorithm for green coal production problem. Inform Sci, 518:256-271.

[10]Deb K, 2001. Nonlinear goal programming using multi-objective genetic algorithms. J Oper Res Soc, 52(3):291-302.

[11]Deb K, Pratap A, Agarwal S, et al., 2002a. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput, 6(2):182-197.

[12]Deb K, Thiele L, Laumanns M, et al., 2002b. Scalable multi-objective optimization test problems. Proc Congress on Evolutionary Computation, p.825-830.

[13]Dong MG, Liu B, Jing C, 2020. A many-objective evolutionary algorithm based on decomposition with dynamic resource allocation for irregular optimization. Front Inform Technol Electron Eng, 21(8):1171-1190.

[14]George T, Amudha T, 2020. Genetic algorithm based multi-objective optimization framework to solve traveling salesman problem. In: Sharma H, Govindan K, Poonia R (Eds.), Advances in Computing and Intelligent Systems: Algorithms for Intelligent Systems. Springer, Singapore.

[15]Huang CZ, Yuan HW, Geng YM, 2021. Multi-objective preference optimization method of permanent magnet assisted reluctance motor. Proc 17^th Int Conf on Computational Intelligence and Security, p.413-419.

[16]Ishibuchi H, Matsumoto T, Masuyama N, et al., 2020. Effects of dominance resistant solutions on the performance of evolutionary multi-objective and many-objective algorithms. Proc Genetic and Evolutionary Computation Conf, p.507-515.

[17]Jakubovski Filho HL, Ferreira TN, Vergilio SR, 2019. Preference based multi-objective algorithms applied to the variability testing of software product lines. J Syst Softw, 151:194-209.

[18]Jiang SW, Zhang J, Ong YS, et al., 2015. A simple and fast hypervolume indicator-based multiobjective evolutionary algorithm. IEEE Trans Cybern, 45(10):2202-2213.

[19]Lai G, Liao MH, Li K, 2021. Empirical studies on the role of the decision maker in interactive evolutionary multi-objective optimization. Proc IEEE Congress on Evolutionary Computation, p.185-192.

[20]Li H, Deng JD, Zhang QF, et al., 2019. Adaptive Epsilon dominance in decomposition-based multiobjective evolutionary algorithm. Swarm Evol Comput, 45:52-67.

[21]Li HR, He FZ, Yan XH, 2019. IBEA-SVM: an indicator-based evolutionary algorithm based on pre-selection with classification guided by SVM. Appl Math A J Chin Univ, 34(1):1-26.

[22]Li LM, Wang YL, Trautmann H, et al., 2018. Multiobjective evolutionary algorithms based on target region preferences. Swarm Evol Comput, 40:196-215.

[23]Lin BR, Chen HZ, Liu YC, et al., 2021. A preference-based multi-objective building performance optimization method for early design stage. Build Simul, 14(3):477-494.

[24]Liu QQ, Jin YC, Heiderich M, et al., 2020. An adaptive reference vector-guided evolutionary algorithm using growing neural gas for many-objective optimization of irregular problems. IEEE Trans Cybern, 52(5):2698-2711.

[25]Liu RC, Song XL, Fang LF, et al., 2017. An r-dominance-based preference multi-objective optimization for many-objective optimization. Soft Comput, 21(17):5003-5024.

[26]López-Jaimes A, Coello CAC, 2014. Including preferences into a multiobjective evolutionary algorithm to deal with many-objective engineering optimization problems. Inform Sci, 277:1-20.

[27]Louis SJ, McDonnell J, 2004. Learning with case-injected genetic algorithms. IEEE Trans Evol Comput, 8(4):316-328.

[28]Luo WJ, Shi LM, Lin X, et al., 2019. The ĝ-dominance relation for preference-based evolutionary multi-objective optimization. Proc IEEE Congress on Evolutionary Computation, p.2418-2425.

[29]Marler RT, Arora JS, 2010. The weighted sum method for multi-objective optimization: new insights. Struct Multidisc Optim, 41(6):853-862.

[30]Menchaca-Méndez A, Montero E, Antonio LM, et al., 2019. A co-evolutionary scheme for multi-objective evolutionary algorithms based on ϵ-dominance. IEEE Access, 7:18267-18283.

[31]Miguel F, Frutos M, Tohmé F, et al., 2019. A decision support tool for urban freight transport planning based on a multi-objective evolutionary algorithm. IEEE Access, 7:156707-156721.

[32]Mohammadi A, Omidvar MN, Li XD, 2013. A new performance metric for user-preference based multi-objective evolutionary algorithms. Proc IEEE Congress on Evolutionary Computation, p.2825-2832.

[33]Paknejad P, Khorsand R, Ramezanpour M, 2021. Chaotic improved PICEA-g-based multi-objective optimization for workflow scheduling in cloud environment. Fut Gener Comput Syst, 117:12-28.

[34]Pirouz B, Khorram E, 2016. A computational approach based on the ϵ-constraint method in multi-objective optimization problems. Adv Appl Stat, 49(6):453-483.

[35]Premkumar M, Jangir P, Kumar BS, et al., 2021. A new arithmetic optimization algorithm for solving real-world multiobjective CEC-2021 constrained optimization problems: diversity analysis and validations. IEEE Access, 9:84263-84295.

[36]Sudeng S, Wattanapongsakorn N, 2013. Adaptive geometric angle-based algorithm with independent objective biasing for pruning Pareto-optimal solutions. Proc Science and Information Conf, p.514-523.

[37]Sudeng S, Wattanapongsakorn N, 2015. Post Pareto-optimal pruning algorithm for multiple objective optimization using specific extended angle dominance. Eng Appl Artif Intell, 38:221-236.

[38]Sun YN, Yen GG, Yi Z, 2019. IGD indicator-based evolutionary algorithm for many-objective optimization problems. IEEE Trans Evol Comput, 23(2):173-187.

[39]Wahid A, Gao XY, Andreae P, 2015. Multi-objective clustering ensemble for high-dimensional data based on strength Pareto evolutionary algorithm (SPEA-II). Proc IEEE Int Conf on Data Science and Advanced Analytics, p.1-9.

[40]Wang F, Li YX, Zhang H, et al., 2019. An adaptive weight vector guided evolutionary algorithm for preference-based multi-objective optimization. Swarm Evol Comput, 49:220-233.

[41]Wang R, Purshouse RC, Fleming PJ, 2013. Preference-inspired co-evolutionary algorithm using adaptively generated goal vectors. Proc IEEE Congress on Evolutionary Computation, p.916-923.

[42]Wang R, Purshouse RC, Giagkiozis I, et al., 2015a. The iPICEA-g: a new hybrid evolutionary multi-criteria decision making approach using the brushing technique. Eur J Oper Res, 243(2):442-453.

[43]Wang R, Purshouse RC, Fleming PJ, 2015b. Preference-inspired co-evolutionary algorithms using weight vectors. Eur J Oper Res, 243(2):423-441.

[44]Yu G, Zheng J, Shen R, et al, 2016. Decomposing the user-preference in multiobjective optimization. Soft Comput, 20(10):4005-4021.

[45]Zhang QF, Li H, 2007. MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput, 11(6):712-731.

[46]Zhang ZX, Chen WN, Jin H, et al., 2021. A preference biobjective evolutionary algorithm for the payment scheduling negotiation problem. IEEE Trans Cybern, 51(12):6105-6118.

[47]Zhao LD, Wang B, Shen CY, 2021. A multi-objective scheduling method for operational coordination time using improved triangular fuzzy number representation. PLoS ONE, 16(6):e0252293.

[48]Zheng JH, Xie ZZ, 2014. A study on how to use angle information to include decision maker's preferences. Acta Electron Sin, 42(11):2239-2246 (in Chinese).

[49]Zheng JH, Lai N, Guo GQ, 2014. ϵ-Pareto dominance strategy based on angle preference in MOEA. PR AI, 27(6):569-576 (in Chinese).

[50]Zitzler E, Künzli S, 2004. Indicator-based selection in multiobjective search. Proc 8^th Int Conf on Parallel Problem Solving from Nature, p.832-842.